It is common practice to utilize various techniques for identifying well and reservoir behavior. To identify such behavior, physical characteristics and parameters of the underground formation are found. The particular underground formation of interest is analyzed by obtaining experimental pressure data over time. This experimental pressure data versus time data can be obtained during the build-up of the well as well as during the drawdown of the well. Using a diagnostic plot of the pressure data as a function of time, a subsequent comparison can be made with theoretical type-curves in order to identify the interpretation model by matching the diagnostic plot with one of the type-curves. After the matching of the diagnostic plot with one of such curves, a verification of the match is typically made. That is, usually by another analysis technique, a check is made to determine whether or not a proper match was made. By way of example, the well-known Horner analysis, or some derived form of the Horner technique, is conducted to determine whether a proper selection or match was made and accurate underground characteristics obtained.
In conjunction with matching the experimental diagnostic plot with one of a series of type-curves, it is common practice to define the type-curves using dimensionless pressure versus dimensionless time wherein each curve of the series of type-curves is distinguishable by a dimensionless number that depends upon the specific reservoir model. Each dimensionless parameter can be defined as the measured or experimental parameter, corresponding to the dimensionless parameter, multiplied by a constant coefficient. The coefficient relates to parameters characterizing the reservoir, the fluid, and the test made in conjunction with obtaining the experimental pressure data. Accordingly, before finding the match between the diagnostic plot and one of the type-curves, a conversion is normally made from dimensioned pressure data to dimensionless pressure data using a constant coefficient.
In connection with the determination of the dimensionless parameters, the derivative of the diagnostic plot of pressure versus time is found and also plotted in using the method of the present invention. The pressure derivative curve is used in finding the pressure match and the time match. The pressure match is defined as being equal to the dimensionless pressure divided by the change in pressure or delta pressure (p.sub.D /delta (p)). While the time match is defined as being equal to the dimensionless time divided by the change in time or delta time, where the definition of dimensionless time depends upon the type-curves being used, e.g., in the case of wellbore storage, dimensionless time=t.sub.D /C.sub.D and in the case of a fractured well, dimensionless time=t.sub.Df. Each of the pressure match and time match values is constant for a particular diagnostic plot. Using each of these two determined constant values, corresponding dimensionless pressure and dimensionless time values can be determined using the experimental pressure data.
The differentiation of the pressure data or points making up the pressure curve has been previously advanced in connection with underground formation analysis. A use of the pressure derivative curve is disclosed in an article entitled "A New Set of Type Curves Simplifies Well Test Analysis" authored by D. Bourdet, T. M. Whittle, A. A. Douglas, and Y. M. Pirard and published in World Oil, May, 1983. This article discusses, among other things, a method for determining pressure match and time match utilizing the pressure derivative curve. This disclosed method, however, depends upon type-curves to determine the pressure match and the time match. Specifically, the method disclosed in the article involves the obtaining of the pressure and time related data and then determining the derivative of the pressure data with respect to dimensionless time over dimensionless wellbore storage (t.sub.D /C.sub.D). Both the pressure and derivative of pressure experimental data are plotted on the same graph. In addition to the pressure and derivative of pressure curves, a graph of a series of type-curves are provided. The type-curves include two sets of curves. A first set relates to a plot of dimensionless pressure (p.sub.D) versus dimensionless time (t.sub.D /C.sub.D) while the second set relates to a plot of the derivative of dimensionless pressure relative to dimensionless time. To determine the pressure match and time match, both the pressure and the pressure derivative experimental data are matched to corresponding type-curves and pressure derivative type-curves. This matching is accomplished by shifting the dimensionless data graph relative to the dimensioned data graph while keeping the axes of the two graphs parallel. The shifting is continued until a fit or match is obtained for both the pressure and the pressure derivative experimental data. After a match is found, a point (match point) is selected by the user and its coordinates are determined or read from both the dimensionless data graph and the dimensioned data graph. From these four values using the four different axes for the two graphs, pressure match and time match can be found since pressure match=p.sub.D /delta (p) and time match=t.sub.D /delta (t).
The foregoing method has certain drawbacks. In order to determine the pressure match and time match, a series of type-curves and the diagnostic plot including the pressure derivative curve must be shifted in order to determine pressure match and time match. Such manipulations may prove to be cumbersome and time-consuming to the user of this analysis technique. The present invention seeks to overcome such deficiencies in providing an improved analytical tool for finding pressure match and time match during the process for evaluating underground formation characteristics.